tau-recurrent sequences and modular forms

Federico Pellarin (1)

1 LA MUSE - Laboratoire de Mathématiques Unifiées de Saint-Etienne

In this paper we deal with Drinfeld modular forms, defined and taking values in complete fields of positive characteristic. Our aim is to study a sequence of families of Drinfeld modular forms depending on a parameter t that produces, for certain values of t, several kinds of Eisenstein series considered by Gekeler. We obtain formulas involving these functions. To obtain our results, we introduce and discuss tau-linear recurrent sequences and deformations of vectorial modular forms in this setting.

Mots clés: Drinfeld modular forms; Tau-linear recurrent sequences; Function fields of positive characteristic

Domaines: Théorie des nombres [math.NT]

Federico Pellarin. tau-recurrent sequences and modular forms. 2011. ⟨hal-00593841v1⟩